%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU129+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:10:42 PM UTC 2026
% Result : Theorem 0.51s 1.60s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 85)
% Comments :
%------------------------------------------------------------------------------
fof(t4_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(t26_xboole_1,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(t3_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(fc2_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(t8_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X3,X2) )
=> subset(set_union2(X1,X3),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(t19_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3) )
=> subset(X1,set_intersection2(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t1_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(t17_xboole_1,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(t12_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t3_xboole_1,lemma,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(idempotence_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(t2_xboole_1,lemma,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_34,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t4_xboole_0]) ).
fof(i_0_35,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
inference(assume_negation,[status(cth)],[t26_xboole_1]) ).
fof(i_0_36,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t3_xboole_0]) ).
fof(i_0_37,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_38,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_39,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_40,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(i_0_41,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_42,plain,
! [X104,X105,X106,X107,X108,X109,X110,X111] :
( ( in(X107,X104)
| ~ in(X107,X106)
| X106 != set_intersection2(X104,X105) )
& ( in(X107,X105)
| ~ in(X107,X106)
| X106 != set_intersection2(X104,X105) )
& ( ~ in(X108,X104)
| ~ in(X108,X105)
| in(X108,X106)
| X106 != set_intersection2(X104,X105) )
& ( ~ in(esk4_3(X109,X110,X111),X111)
| ~ in(esk4_3(X109,X110,X111),X109)
| ~ in(esk4_3(X109,X110,X111),X110)
| X111 = set_intersection2(X109,X110) )
& ( in(esk4_3(X109,X110,X111),X109)
| in(esk4_3(X109,X110,X111),X111)
| X111 = set_intersection2(X109,X110) )
& ( in(esk4_3(X109,X110,X111),X110)
| in(esk4_3(X109,X110,X111),X111)
| X111 = set_intersection2(X109,X110) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_xboole_0])])])])])]) ).
fof(i_0_43,plain,
! [X89,X90,X91,X92,X93,X94,X95,X96] :
( ( ~ in(X92,X91)
| in(X92,X89)
| in(X92,X90)
| X91 != set_union2(X89,X90) )
& ( ~ in(X93,X89)
| in(X93,X91)
| X91 != set_union2(X89,X90) )
& ( ~ in(X93,X90)
| in(X93,X91)
| X91 != set_union2(X89,X90) )
& ( ~ in(esk2_3(X94,X95,X96),X94)
| ~ in(esk2_3(X94,X95,X96),X96)
| X96 = set_union2(X94,X95) )
& ( ~ in(esk2_3(X94,X95,X96),X95)
| ~ in(esk2_3(X94,X95,X96),X96)
| X96 = set_union2(X94,X95) )
& ( in(esk2_3(X94,X95,X96),X96)
| in(esk2_3(X94,X95,X96),X94)
| in(esk2_3(X94,X95,X96),X95)
| X96 = set_union2(X94,X95) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_xboole_0])])])])])]) ).
fof(i_0_44,lemma,
! [X149,X150,X152,X153,X154] :
( ( disjoint(X149,X150)
| in(esk11_2(X149,X150),set_intersection2(X149,X150)) )
& ( ~ in(X154,set_intersection2(X152,X153))
| ~ disjoint(X152,X153) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_34])])])])]) ).
fof(i_0_45,lemma,
! [X162,X163,X164] :
( ~ subset(X162,X163)
| ~ subset(X164,X163)
| subset(set_union2(X162,X164),X163) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_xboole_1])]) ).
fof(i_0_46,lemma,
! [X130,X131,X132] :
( ~ subset(X130,X131)
| ~ subset(X130,X132)
| subset(X130,set_intersection2(X131,X132)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])]) ).
fof(i_0_47,negated_conjecture,
( subset(esk7_0,esk8_0)
& ~ subset(set_intersection2(esk7_0,esk9_0),set_intersection2(esk8_0,esk9_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_35])])]) ).
fof(i_0_48,plain,
! [X98,X99,X100,X101,X102] :
( ( ~ subset(X98,X99)
| ~ in(X100,X98)
| in(X100,X99) )
& ( in(esk3_2(X101,X102),X101)
| subset(X101,X102) )
& ( ~ in(esk3_2(X101,X102),X102)
| subset(X101,X102) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).
fof(i_0_49,lemma,
! [X142,X143,X145,X146,X147] :
( ( in(esk10_2(X142,X143),X142)
| disjoint(X142,X143) )
& ( in(esk10_2(X142,X143),X143)
| disjoint(X142,X143) )
& ( ~ in(X147,X145)
| ~ in(X147,X146)
| ~ disjoint(X145,X146) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_36])])])])])]) ).
fof(i_0_50,lemma,
! [X134,X135,X136] :
( ~ subset(X134,X135)
| ~ subset(X135,X136)
| subset(X134,X136) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(i_0_51,plain,
! [X115,X116] :
( empty(X115)
| ~ empty(set_union2(X115,X116)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_37])]) ).
fof(i_0_52,plain,
! [X117,X118] :
( empty(X117)
| ~ empty(set_union2(X118,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_38])]) ).
fof(i_0_53,plain,
! [X83,X84] :
( ( subset(X83,X84)
| X83 != X84 )
& ( subset(X84,X83)
| X83 != X84 )
& ( ~ subset(X83,X84)
| ~ subset(X84,X83)
| X83 = X84 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
fof(i_0_54,plain,
! [X77,X78] :
( ~ in(X77,X78)
| ~ in(X78,X77) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_39])]) ).
fof(i_0_55,lemma,
! [X128,X129] : subset(set_intersection2(X128,X129),X128),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(i_0_56,lemma,
! [X158,X159] : subset(X158,set_union2(X158,X159)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(i_0_57,lemma,
! [X126,X127] :
( ~ subset(X126,X127)
| set_union2(X126,X127) = X127 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
fof(i_0_58,plain,
! [X124,X125] :
( ~ disjoint(X124,X125)
| disjoint(X125,X124) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(i_0_59,plain,
! [X113,X114] :
( ( ~ disjoint(X113,X114)
| set_intersection2(X113,X114) = empty_set )
& ( set_intersection2(X113,X114) != empty_set
| disjoint(X113,X114) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
fof(i_0_60,plain,
! [X156,X157] :
( ~ in(X156,X157)
| ~ empty(X157) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_61,plain,
! [X81,X82] : set_intersection2(X81,X82) = set_intersection2(X82,X81),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_62,plain,
! [X79,X80] : set_union2(X79,X80) = set_union2(X80,X79),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_63,plain,
! [X85,X86,X87] :
( ( X85 != empty_set
| ~ in(X86,X85) )
& ( in(esk1_1(X87),X87)
| X87 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_40])])])])]) ).
fof(i_0_64,lemma,
! [X148] :
( ~ subset(X148,empty_set)
| X148 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
fof(i_0_65,plain,
! [X160,X161] :
( ~ empty(X160)
| X160 = X161
| ~ empty(X161) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_66,plain,
! [X120] : set_intersection2(X120,X120) = X120,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_67,plain,
! [X119] : set_union2(X119,X119) = X119,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_68,plain,
! [X123] : subset(X123,X123),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_69,plain,
! [X133] : set_union2(X133,empty_set) = X133,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(i_0_70,lemma,
! [X141] : subset(empty_set,X141),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(i_0_71,plain,
! [X140] : set_intersection2(X140,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(i_0_72,plain,
! [X155] :
( ~ empty(X155)
| X155 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_73,plain,
~ empty(esk6_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_41])]) ).
fof(i_0_74,plain,
empty(esk5_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_75,plain,
( X3 = set_intersection2(X1,X2)
| ~ in(esk4_3(X1,X2,X3),X3)
| ~ in(esk4_3(X1,X2,X3),X1)
| ~ in(esk4_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_76,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk2_3(X1,X2,X3),X1)
| ~ in(esk2_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_77,plain,
( X3 = set_union2(X1,X2)
| ~ in(esk2_3(X1,X2,X3),X2)
| ~ in(esk2_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_78,plain,
( in(esk2_3(X1,X2,X3),X3)
| in(esk2_3(X1,X2,X3),X1)
| in(esk2_3(X1,X2,X3),X2)
| X3 = set_union2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_79,plain,
( in(esk4_3(X1,X2,X3),X1)
| in(esk4_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_80,plain,
( in(esk4_3(X1,X2,X3),X2)
| in(esk4_3(X1,X2,X3),X3)
| X3 = set_intersection2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_81,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_82,lemma,
( subset(set_union2(X1,X3),X2)
| ~ subset(X1,X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_83,lemma,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_84,negated_conjecture,
~ subset(set_intersection2(esk7_0,esk9_0),set_intersection2(esk8_0,esk9_0)),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_85,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_86,lemma,
( disjoint(X1,X2)
| in(esk11_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_87,plain,
( subset(X1,X2)
| ~ in(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_88,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_89,lemma,
( ~ in(X1,X2)
| ~ in(X1,X3)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_90,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_91,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_92,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_93,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_94,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_95,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_96,lemma,
( in(esk10_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_97,lemma,
( in(esk10_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_98,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_99,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_100,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_101,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_102,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_103,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_104,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_105,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_106,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_107,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_108,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_109,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_110,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_111,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_112,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_113,plain,
( in(esk1_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_114,lemma,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_115,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_116,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_117,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_118,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_119,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_120,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_121,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_122,lemma,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_123,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_124,negated_conjecture,
subset(esk7_0,esk8_0),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_125,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_126,plain,
~ empty(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_127,plain,
empty(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_128,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_129,axiom,
X1 = X1 ).
cnf(i_0_130,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_131,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_132,axiom,
( X1 != X2
| set_intersection2(X1,X3) = set_intersection2(X2,X3) ) ).
cnf(i_0_133,axiom,
( X1 != X2
| set_intersection2(X3,X1) = set_intersection2(X3,X2) ) ).
cnf(i_0_134,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_135,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_136,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_137,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_138,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_139,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_140,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_141,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_142,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_129_001,axiom,
X1 = X1 ).
cnf(i_0_130_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_131_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_132_004,axiom,
( X1 != X2
| set_intersection2(X1,X3) = set_intersection2(X2,X3) ) ).
cnf(i_0_133_005,axiom,
( X1 != X2
| set_intersection2(X3,X1) = set_intersection2(X3,X2) ) ).
cnf(i_0_134_006,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_135_007,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_136_008,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_137_009,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_138_010,axiom,
( X1 != X2
| ~ disjoint(X1,X3)
| disjoint(X2,X3) ) ).
cnf(i_0_139_011,axiom,
( X1 != X2
| ~ disjoint(X3,X1)
| disjoint(X3,X2) ) ).
cnf(i_0_140_012,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_141_013,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_142_014,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_143,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X2)
| ~ in(X1,X3) ),
inference(equality_inference,[],[85]) ).
cnf(i_0_144,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X2,X3)) ),
inference(equality_inference,[],[88]) ).
cnf(i_0_145,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(equality_inference,[],[90]) ).
cnf(i_0_146,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(equality_inference,[],[91]) ).
cnf(i_0_147,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X2) ),
inference(equality_inference,[],[92]) ).
cnf(i_0_148,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(equality_inference,[],[93]) ).
cnf(i_0_149,plain,
~ in(X1,empty_set),
inference(equality_inference,[],[112]) ).
cnf(i_0_150,plain,
subset(X1,X1),
inference(equality_inference,[],[115]) ).
cnf(i_0_151,plain,
subset(X1,X1),
inference(equality_inference,[],[116]) ).
cnf(i_0_152,plain,
subset(set_union2(X1,X1),X1),
inference(scs_inference,[],[i_0_119,i_0_115]) ).
cnf(i_0_153,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_115]) ).
cnf(i_0_154,plain,
subset(X1,set_intersection2(X1,X1)),
inference(scs_inference,[],[i_0_118,i_0_119,i_0_115,i_0_116]) ).
cnf(i_0_155,plain,
( X1 != X2
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_116]) ).
cnf(i_0_156,plain,
disjoint(empty_set,X1),
inference(scs_inference,[],[i_0_149,i_0_118,i_0_119,i_0_115,i_0_116,i_0_96]) ).
cnf(i_0_157,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_158,plain,
( in(esk10_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_96]) ).
cnf(i_0_159,plain,
disjoint(X1,empty_set),
inference(scs_inference,[],[i_0_149,i_0_157,i_0_118,i_0_119,i_0_115,i_0_116,i_0_96,i_0_97]) ).
cnf(i_0_160,plain,
~ in(X1,empty_set),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_161,plain,
( in(esk10_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_97]) ).
cnf(i_0_162,plain,
~ in(X1,esk5_0),
inference(scs_inference,[],[i_0_149,i_0_157,i_0_118,i_0_119,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109]) ).
cnf(i_0_163,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_109]) ).
cnf(i_0_164,plain,
~ in(X1,set_intersection2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_149,i_0_157,i_0_118,i_0_119,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112]) ).
cnf(i_0_165,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_118]) ).
cnf(i_0_166,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_112]) ).
cnf(i_0_167,plain,
set_intersection2(empty_set,X1) = empty_set,
inference(scs_inference,[],[i_0_103,i_0_149,i_0_157,i_0_118,i_0_119,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114]) ).
cnf(i_0_168,plain,
subset(set_intersection2(X1,X2),X1),
inference(rename_variables,[],[i_0_103]) ).
cnf(i_0_169,plain,
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_170,plain,
~ in(X1,set_intersection2(empty_set,X2)),
inference(scs_inference,[],[i_0_103,i_0_149,i_0_157,i_0_160,i_0_118,i_0_119,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145]) ).
cnf(i_0_171,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(rename_variables,[],[i_0_145]) ).
cnf(i_0_172,plain,
~ in(X1,set_intersection2(X2,empty_set)),
inference(scs_inference,[],[i_0_103,i_0_149,i_0_157,i_0_160,i_0_118,i_0_119,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145,i_0_146]) ).
cnf(i_0_173,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(rename_variables,[],[i_0_146]) ).
cnf(i_0_174,plain,
X1 = set_intersection2(X1,X1),
inference(scs_inference,[],[i_0_103,i_0_149,i_0_157,i_0_160,i_0_118,i_0_165,i_0_119,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145,i_0_146,i_0_130]) ).
cnf(i_0_175,plain,
subset(set_intersection2(esk7_0,X1),esk8_0),
inference(scs_inference,[],[i_0_124,i_0_103,i_0_168,i_0_149,i_0_157,i_0_160,i_0_118,i_0_165,i_0_119,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145,i_0_146,i_0_130,i_0_94]) ).
cnf(i_0_176,plain,
subset(set_intersection2(X1,X2),X1),
inference(rename_variables,[],[i_0_103]) ).
cnf(i_0_177,plain,
( ~ subset(X1,X2)
| subset(X3,X2)
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_94]) ).
cnf(i_0_178,plain,
empty_set = set_intersection2(empty_set,X1),
inference(scs_inference,[],[i_0_124,i_0_103,i_0_168,i_0_176,i_0_122,i_0_149,i_0_157,i_0_160,i_0_118,i_0_165,i_0_119,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145,i_0_146,i_0_130,i_0_94,i_0_101]) ).
cnf(i_0_179,plain,
subset(empty_set,X1),
inference(rename_variables,[],[i_0_122]) ).
cnf(i_0_180,plain,
subset(set_intersection2(X1,X2),X1),
inference(rename_variables,[],[i_0_103]) ).
cnf(i_0_181,plain,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_101]) ).
cnf(i_0_182,plain,
~ subset(set_intersection2(set_intersection2(esk7_0,esk9_0),set_intersection2(esk7_0,esk9_0)),set_intersection2(esk8_0,esk9_0)),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_103,i_0_168,i_0_176,i_0_122,i_0_149,i_0_157,i_0_160,i_0_118,i_0_165,i_0_119,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145,i_0_146,i_0_130,i_0_94,i_0_101,i_0_140]) ).
cnf(i_0_183,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_118]) ).
cnf(i_0_184,plain,
~ subset(set_intersection2(esk7_0,esk9_0),set_intersection2(set_intersection2(esk8_0,esk9_0),set_intersection2(esk8_0,esk9_0))),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_103,i_0_168,i_0_176,i_0_122,i_0_149,i_0_157,i_0_160,i_0_118,i_0_165,i_0_183,i_0_119,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145,i_0_146,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141]) ).
cnf(i_0_185,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_118]) ).
cnf(i_0_186,plain,
~ in(X1,set_intersection2(set_intersection2(empty_set,X2),set_intersection2(empty_set,X2))),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_103,i_0_168,i_0_176,i_0_122,i_0_149,i_0_157,i_0_160,i_0_118,i_0_165,i_0_183,i_0_185,i_0_119,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145,i_0_146,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_90]) ).
cnf(i_0_187,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_118]) ).
cnf(i_0_188,plain,
( X1 != set_intersection2(X2,X3)
| in(X4,X2)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_189,plain,
~ in(X1,set_intersection2(set_intersection2(X2,empty_set),set_intersection2(X2,empty_set))),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_103,i_0_168,i_0_176,i_0_122,i_0_149,i_0_157,i_0_160,i_0_118,i_0_165,i_0_183,i_0_185,i_0_187,i_0_119,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145,i_0_146,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_90,i_0_91]) ).
cnf(i_0_190,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_118]) ).
cnf(i_0_191,plain,
( X1 != set_intersection2(X2,X3)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_91]) ).
cnf(i_0_192,plain,
set_union2(set_intersection2(X1,X1),set_intersection2(X1,X1)) = X1,
inference(scs_inference,[],[i_0_84,i_0_124,i_0_103,i_0_168,i_0_176,i_0_122,i_0_149,i_0_157,i_0_160,i_0_118,i_0_165,i_0_183,i_0_185,i_0_187,i_0_190,i_0_119,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145,i_0_146,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_90,i_0_91,i_0_131]) ).
cnf(i_0_193,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_194,plain,
~ in(X1,set_intersection2(esk5_0,esk5_0)),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_103,i_0_168,i_0_176,i_0_122,i_0_149,i_0_157,i_0_160,i_0_118,i_0_165,i_0_183,i_0_185,i_0_187,i_0_190,i_0_119,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145,i_0_146,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_90,i_0_91,i_0_131,i_0_137]) ).
cnf(i_0_195,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_118]) ).
cnf(i_0_196,plain,
esk5_0 != esk6_0,
inference(scs_inference,[],[i_0_84,i_0_124,i_0_103,i_0_168,i_0_176,i_0_122,i_0_149,i_0_157,i_0_160,i_0_118,i_0_165,i_0_183,i_0_185,i_0_187,i_0_190,i_0_119,i_0_126,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145,i_0_146,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_90,i_0_91,i_0_131,i_0_137,i_0_142]) ).
cnf(i_0_197,plain,
~ in(X1,set_intersection2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_103,i_0_168,i_0_176,i_0_122,i_0_149,i_0_157,i_0_160,i_0_118,i_0_165,i_0_183,i_0_185,i_0_187,i_0_190,i_0_195,i_0_119,i_0_126,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145,i_0_146,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_90,i_0_91,i_0_131,i_0_137,i_0_142,i_0_88]) ).
cnf(i_0_198,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_118]) ).
cnf(i_0_199,plain,
( X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_88]) ).
cnf(i_0_200,plain,
subset(esk5_0,X1),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_103,i_0_168,i_0_176,i_0_122,i_0_149,i_0_157,i_0_160,i_0_118,i_0_165,i_0_183,i_0_185,i_0_187,i_0_190,i_0_195,i_0_119,i_0_126,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145,i_0_146,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_90,i_0_91,i_0_131,i_0_137,i_0_142,i_0_88,i_0_98]) ).
cnf(i_0_201,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_98]) ).
cnf(i_0_202,plain,
disjoint(set_intersection2(empty_set,X1),set_intersection2(empty_set,X1)),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_103,i_0_168,i_0_176,i_0_122,i_0_149,i_0_157,i_0_160,i_0_118,i_0_165,i_0_183,i_0_185,i_0_187,i_0_190,i_0_195,i_0_119,i_0_126,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145,i_0_146,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_90,i_0_91,i_0_131,i_0_137,i_0_142,i_0_88,i_0_98,i_0_86]) ).
cnf(i_0_203,plain,
( in(esk11_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_204,plain,
~ subset(set_intersection2(esk7_0,esk9_0),esk9_0),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_103,i_0_168,i_0_176,i_0_122,i_0_149,i_0_157,i_0_160,i_0_118,i_0_165,i_0_183,i_0_185,i_0_187,i_0_190,i_0_195,i_0_119,i_0_126,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145,i_0_146,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_90,i_0_91,i_0_131,i_0_137,i_0_142,i_0_88,i_0_98,i_0_86,i_0_83]) ).
cnf(i_0_205,plain,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_206,plain,
( in(X1,set_union2(set_union2(X2,X3),set_union2(X2,X3)))
| ~ in(X1,X2) ),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_103,i_0_168,i_0_176,i_0_122,i_0_149,i_0_157,i_0_160,i_0_118,i_0_165,i_0_183,i_0_185,i_0_187,i_0_190,i_0_195,i_0_119,i_0_193,i_0_126,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145,i_0_146,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_90,i_0_91,i_0_131,i_0_137,i_0_142,i_0_88,i_0_98,i_0_86,i_0_83,i_0_92]) ).
cnf(i_0_207,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_208,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_92]) ).
cnf(i_0_209,plain,
( in(X1,set_union2(set_union2(X2,X3),set_union2(X2,X3)))
| ~ in(set_intersection2(X1,X1),X2) ),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_103,i_0_168,i_0_176,i_0_122,i_0_149,i_0_157,i_0_160,i_0_118,i_0_165,i_0_183,i_0_185,i_0_187,i_0_190,i_0_195,i_0_198,i_0_119,i_0_193,i_0_126,i_0_127,i_0_115,i_0_116,i_0_96,i_0_97,i_0_109,i_0_112,i_0_114,i_0_145,i_0_146,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_90,i_0_91,i_0_131,i_0_137,i_0_142,i_0_88,i_0_98,i_0_86,i_0_83,i_0_92,i_0_136]) ).
cnf(i_0_210,plain,
( ~ disjoint(X1,X2)
| ~ in(X3,X1)
| ~ in(X3,X2) ),
inference(rename_variables,[],[i_0_89]) ).
cnf(i_0_211,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_118]) ).
cnf(i_0_213,plain,
subset(set_intersection2(X1,X2),set_intersection2(X2,X1)),
inference(scs_inference,[],[i_0_110,i_0_116]) ).
cnf(i_0_214,plain,
( X1 != X2
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_116]) ).
cnf(i_0_215,plain,
~ in(X1,set_intersection2(set_intersection2(empty_set,X2),X3)),
inference(scs_inference,[],[i_0_110,i_0_170,i_0_116,i_0_145]) ).
cnf(i_0_216,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(rename_variables,[],[i_0_145]) ).
cnf(i_0_217,plain,
~ in(X1,set_intersection2(X2,set_intersection2(empty_set,X3))),
inference(scs_inference,[],[i_0_110,i_0_170,i_0_116,i_0_145,i_0_146]) ).
cnf(i_0_218,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(rename_variables,[],[i_0_146]) ).
cnf(i_0_219,plain,
subset(set_intersection2(X1,empty_set),empty_set),
inference(scs_inference,[],[i_0_110,i_0_123,i_0_170,i_0_116,i_0_145,i_0_146,i_0_115]) ).
cnf(i_0_220,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_115]) ).
cnf(i_0_221,plain,
~ in(X1,set_union2(set_intersection2(empty_set,empty_set),set_intersection2(empty_set,empty_set))),
inference(scs_inference,[],[i_0_110,i_0_123,i_0_192,i_0_170,i_0_116,i_0_145,i_0_146,i_0_115,i_0_112]) ).
cnf(i_0_222,plain,
set_union2(set_intersection2(X1,X1),set_intersection2(X1,X1)) = X1,
inference(rename_variables,[],[i_0_192]) ).
cnf(i_0_223,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_112]) ).
cnf(i_0_224,plain,
esk5_0 = empty_set,
inference(scs_inference,[],[i_0_200,i_0_110,i_0_123,i_0_192,i_0_170,i_0_116,i_0_145,i_0_146,i_0_115,i_0_112,i_0_114]) ).
cnf(i_0_225,plain,
subset(esk5_0,X1),
inference(rename_variables,[],[i_0_200]) ).
cnf(i_0_226,plain,
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_227,plain,
subset(set_intersection2(empty_set,X1),X2),
inference(scs_inference,[],[i_0_200,i_0_110,i_0_123,i_0_192,i_0_170,i_0_116,i_0_145,i_0_146,i_0_115,i_0_112,i_0_114,i_0_98]) ).
cnf(i_0_228,plain,
~ in(X1,set_intersection2(empty_set,X2)),
inference(rename_variables,[],[i_0_170]) ).
cnf(i_0_229,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_98]) ).
cnf(i_0_230,plain,
disjoint(set_intersection2(X1,empty_set),set_intersection2(X1,empty_set)),
inference(scs_inference,[],[i_0_200,i_0_110,i_0_123,i_0_192,i_0_189,i_0_170,i_0_116,i_0_145,i_0_146,i_0_115,i_0_112,i_0_114,i_0_98,i_0_86]) ).
cnf(i_0_231,plain,
~ in(X1,set_intersection2(set_intersection2(X2,empty_set),set_intersection2(X2,empty_set))),
inference(rename_variables,[],[i_0_189]) ).
cnf(i_0_232,plain,
( in(esk11_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_233,plain,
disjoint(set_intersection2(empty_set,X1),X2),
inference(scs_inference,[],[i_0_200,i_0_110,i_0_123,i_0_192,i_0_189,i_0_170,i_0_228,i_0_116,i_0_145,i_0_146,i_0_115,i_0_112,i_0_114,i_0_98,i_0_86,i_0_96]) ).
cnf(i_0_234,plain,
~ in(X1,set_intersection2(empty_set,X2)),
inference(rename_variables,[],[i_0_170]) ).
cnf(i_0_235,plain,
( in(esk10_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_96]) ).
cnf(i_0_236,plain,
disjoint(X1,set_intersection2(empty_set,X2)),
inference(scs_inference,[],[i_0_200,i_0_110,i_0_123,i_0_192,i_0_189,i_0_170,i_0_228,i_0_234,i_0_116,i_0_145,i_0_146,i_0_115,i_0_112,i_0_114,i_0_98,i_0_86,i_0_96,i_0_97]) ).
cnf(i_0_237,plain,
~ in(X1,set_intersection2(empty_set,X2)),
inference(rename_variables,[],[i_0_170]) ).
cnf(i_0_238,plain,
( in(esk10_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_97]) ).
cnf(i_0_239,plain,
empty_set = set_intersection2(X1,empty_set),
inference(scs_inference,[],[i_0_200,i_0_110,i_0_123,i_0_192,i_0_189,i_0_170,i_0_228,i_0_234,i_0_116,i_0_145,i_0_146,i_0_115,i_0_112,i_0_114,i_0_98,i_0_86,i_0_96,i_0_97,i_0_130]) ).
cnf(i_0_240,plain,
subset(set_union2(esk7_0,esk7_0),esk8_0),
inference(scs_inference,[],[i_0_124,i_0_152,i_0_200,i_0_110,i_0_123,i_0_192,i_0_189,i_0_170,i_0_228,i_0_234,i_0_116,i_0_145,i_0_146,i_0_115,i_0_112,i_0_114,i_0_98,i_0_86,i_0_96,i_0_97,i_0_130,i_0_94]) ).
cnf(i_0_241,plain,
subset(set_union2(X1,X1),X1),
inference(rename_variables,[],[i_0_152]) ).
cnf(i_0_242,plain,
( ~ subset(X1,X2)
| subset(X3,X2)
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_94]) ).
cnf(i_0_243,plain,
esk5_0 = set_union2(esk5_0,esk5_0),
inference(scs_inference,[],[i_0_124,i_0_152,i_0_241,i_0_200,i_0_225,i_0_110,i_0_123,i_0_192,i_0_189,i_0_170,i_0_228,i_0_234,i_0_116,i_0_145,i_0_146,i_0_115,i_0_112,i_0_114,i_0_98,i_0_86,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101]) ).
cnf(i_0_244,plain,
subset(esk5_0,X1),
inference(rename_variables,[],[i_0_200]) ).
cnf(i_0_245,plain,
subset(set_union2(X1,X1),X1),
inference(rename_variables,[],[i_0_152]) ).
cnf(i_0_246,plain,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_101]) ).
cnf(i_0_247,plain,
~ subset(set_intersection2(esk9_0,esk7_0),set_intersection2(esk8_0,esk9_0)),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_152,i_0_241,i_0_200,i_0_225,i_0_110,i_0_123,i_0_192,i_0_189,i_0_170,i_0_228,i_0_234,i_0_116,i_0_145,i_0_146,i_0_115,i_0_112,i_0_114,i_0_98,i_0_86,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101,i_0_140]) ).
cnf(i_0_248,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(rename_variables,[],[i_0_110]) ).
cnf(i_0_249,plain,
~ subset(set_intersection2(esk7_0,esk9_0),set_intersection2(esk9_0,esk8_0)),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_152,i_0_241,i_0_200,i_0_225,i_0_110,i_0_248,i_0_123,i_0_192,i_0_189,i_0_170,i_0_228,i_0_234,i_0_116,i_0_145,i_0_146,i_0_115,i_0_112,i_0_114,i_0_98,i_0_86,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141]) ).
cnf(i_0_250,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(rename_variables,[],[i_0_110]) ).
cnf(i_0_251,plain,
set_intersection2(X1,empty_set) = set_intersection2(empty_set,X2),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_152,i_0_241,i_0_200,i_0_225,i_0_178,i_0_110,i_0_248,i_0_123,i_0_192,i_0_189,i_0_170,i_0_228,i_0_234,i_0_116,i_0_145,i_0_146,i_0_115,i_0_112,i_0_114,i_0_98,i_0_86,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131]) ).
cnf(i_0_252,plain,
empty_set != esk6_0,
inference(scs_inference,[],[i_0_84,i_0_124,i_0_152,i_0_241,i_0_200,i_0_225,i_0_178,i_0_110,i_0_248,i_0_123,i_0_192,i_0_189,i_0_170,i_0_228,i_0_234,i_0_128,i_0_126,i_0_116,i_0_145,i_0_146,i_0_115,i_0_112,i_0_114,i_0_98,i_0_86,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131,i_0_142]) ).
cnf(i_0_253,plain,
~ in(X1,set_union2(set_intersection2(esk5_0,esk5_0),set_intersection2(esk5_0,esk5_0))),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_152,i_0_241,i_0_200,i_0_225,i_0_178,i_0_110,i_0_248,i_0_123,i_0_192,i_0_222,i_0_189,i_0_170,i_0_228,i_0_234,i_0_162,i_0_128,i_0_126,i_0_116,i_0_145,i_0_146,i_0_115,i_0_112,i_0_114,i_0_98,i_0_86,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131,i_0_142,i_0_137]) ).
cnf(i_0_254,plain,
set_union2(set_intersection2(X1,X1),set_intersection2(X1,X1)) = X1,
inference(rename_variables,[],[i_0_192]) ).
cnf(i_0_255,plain,
( in(X1,set_union2(set_union2(X2,X3),empty_set))
| ~ in(X1,X3) ),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_152,i_0_241,i_0_200,i_0_225,i_0_178,i_0_110,i_0_248,i_0_123,i_0_192,i_0_222,i_0_189,i_0_170,i_0_228,i_0_234,i_0_162,i_0_121,i_0_128,i_0_126,i_0_116,i_0_145,i_0_146,i_0_115,i_0_112,i_0_114,i_0_98,i_0_86,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131,i_0_142,i_0_137,i_0_93]) ).
cnf(i_0_256,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_121]) ).
cnf(i_0_257,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(rename_variables,[],[i_0_93]) ).
cnf(i_0_258,plain,
~ subset(set_intersection2(esk9_0,esk7_0),esk8_0),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_152,i_0_241,i_0_200,i_0_225,i_0_178,i_0_103,i_0_110,i_0_248,i_0_123,i_0_192,i_0_222,i_0_189,i_0_170,i_0_228,i_0_234,i_0_162,i_0_121,i_0_128,i_0_126,i_0_116,i_0_145,i_0_146,i_0_115,i_0_112,i_0_114,i_0_98,i_0_86,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131,i_0_142,i_0_137,i_0_93,i_0_83]) ).
cnf(i_0_259,plain,
subset(set_intersection2(X1,X2),X1),
inference(rename_variables,[],[i_0_103]) ).
cnf(i_0_260,plain,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_261,plain,
( in(set_intersection2(empty_set,X1),set_union2(set_union2(X2,X3),empty_set))
| ~ in(empty_set,X3) ),
inference(scs_inference,[],[i_0_84,i_0_124,i_0_152,i_0_241,i_0_200,i_0_225,i_0_178,i_0_103,i_0_110,i_0_248,i_0_123,i_0_192,i_0_222,i_0_189,i_0_170,i_0_228,i_0_234,i_0_162,i_0_121,i_0_128,i_0_126,i_0_116,i_0_145,i_0_146,i_0_115,i_0_112,i_0_114,i_0_98,i_0_86,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131,i_0_142,i_0_137,i_0_93,i_0_83,i_0_136]) ).
cnf(i_0_262,plain,
( ~ disjoint(X1,X2)
| ~ in(X3,X1)
| ~ in(X3,X2) ),
inference(rename_variables,[],[i_0_89]) ).
cnf(i_0_264,plain,
~ in(X1,set_intersection2(set_intersection2(X2,empty_set),X3)),
inference(scs_inference,[],[i_0_172,i_0_145]) ).
cnf(i_0_265,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(rename_variables,[],[i_0_145]) ).
cnf(i_0_266,plain,
~ in(X1,set_intersection2(X2,set_intersection2(X3,empty_set))),
inference(scs_inference,[],[i_0_172,i_0_145,i_0_146]) ).
cnf(i_0_267,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(rename_variables,[],[i_0_146]) ).
cnf(i_0_268,plain,
subset(set_union2(X1,X2),set_union2(X2,X1)),
inference(scs_inference,[],[i_0_111,i_0_172,i_0_145,i_0_146,i_0_116]) ).
cnf(i_0_269,plain,
( X1 != X2
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_116]) ).
cnf(i_0_270,plain,
subset(set_intersection2(X1,empty_set),X2),
inference(scs_inference,[],[i_0_111,i_0_172,i_0_145,i_0_146,i_0_116,i_0_98]) ).
cnf(i_0_271,plain,
~ in(X1,set_intersection2(X2,empty_set)),
inference(rename_variables,[],[i_0_172]) ).
cnf(i_0_272,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_98]) ).
cnf(i_0_273,plain,
subset(set_union2(set_intersection2(X1,X1),set_intersection2(X1,X1)),X1),
inference(scs_inference,[],[i_0_111,i_0_172,i_0_192,i_0_145,i_0_146,i_0_116,i_0_98,i_0_115]) ).
cnf(i_0_274,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_115]) ).
cnf(i_0_275,plain,
disjoint(set_intersection2(X1,empty_set),X2),
inference(scs_inference,[],[i_0_111,i_0_172,i_0_271,i_0_192,i_0_145,i_0_146,i_0_116,i_0_98,i_0_115,i_0_96]) ).
cnf(i_0_276,plain,
~ in(X1,set_intersection2(X2,empty_set)),
inference(rename_variables,[],[i_0_172]) ).
cnf(i_0_277,plain,
( in(esk10_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_96]) ).
cnf(i_0_278,plain,
disjoint(X1,set_intersection2(X2,empty_set)),
inference(scs_inference,[],[i_0_111,i_0_172,i_0_271,i_0_276,i_0_192,i_0_145,i_0_146,i_0_116,i_0_98,i_0_115,i_0_96,i_0_97]) ).
cnf(i_0_279,plain,
~ in(X1,set_intersection2(X2,empty_set)),
inference(rename_variables,[],[i_0_172]) ).
cnf(i_0_280,plain,
( in(esk10_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_97]) ).
cnf(i_0_281,plain,
~ in(X1,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_111,i_0_172,i_0_271,i_0_276,i_0_119,i_0_192,i_0_145,i_0_146,i_0_116,i_0_98,i_0_115,i_0_96,i_0_97,i_0_112]) ).
cnf(i_0_282,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_283,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_112]) ).
cnf(i_0_284,plain,
disjoint(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_111,i_0_172,i_0_271,i_0_276,i_0_119,i_0_197,i_0_192,i_0_145,i_0_146,i_0_116,i_0_98,i_0_115,i_0_96,i_0_97,i_0_112,i_0_86]) ).
cnf(i_0_285,plain,
~ in(X1,set_intersection2(set_union2(empty_set,empty_set),set_union2(empty_set,empty_set))),
inference(rename_variables,[],[i_0_197]) ).
cnf(i_0_286,plain,
( in(esk11_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_287,plain,
X1 = set_union2(X1,X1),
inference(scs_inference,[],[i_0_111,i_0_172,i_0_271,i_0_276,i_0_119,i_0_282,i_0_197,i_0_192,i_0_145,i_0_146,i_0_116,i_0_98,i_0_115,i_0_96,i_0_97,i_0_112,i_0_86,i_0_130]) ).
cnf(i_0_288,plain,
~ subset(set_intersection2(esk9_0,esk7_0),esk7_0),
inference(scs_inference,[],[i_0_124,i_0_258,i_0_111,i_0_172,i_0_271,i_0_276,i_0_119,i_0_282,i_0_197,i_0_192,i_0_145,i_0_146,i_0_116,i_0_98,i_0_115,i_0_96,i_0_97,i_0_112,i_0_86,i_0_130,i_0_94]) ).
cnf(i_0_289,plain,
( ~ subset(X1,X2)
| subset(X3,X2)
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_94]) ).
cnf(i_0_290,plain,
esk5_0 = set_intersection2(empty_set,X1),
inference(scs_inference,[],[i_0_124,i_0_227,i_0_258,i_0_200,i_0_111,i_0_172,i_0_271,i_0_276,i_0_119,i_0_282,i_0_197,i_0_192,i_0_145,i_0_146,i_0_116,i_0_98,i_0_115,i_0_96,i_0_97,i_0_112,i_0_86,i_0_130,i_0_94,i_0_101]) ).
cnf(i_0_291,plain,
subset(esk5_0,X1),
inference(rename_variables,[],[i_0_200]) ).
cnf(i_0_292,plain,
subset(set_intersection2(empty_set,X1),X2),
inference(rename_variables,[],[i_0_227]) ).
cnf(i_0_293,plain,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_101]) ).
cnf(i_0_294,plain,
~ subset(set_intersection2(set_intersection2(esk7_0,esk9_0),set_intersection2(esk7_0,esk9_0)),esk9_0),
inference(scs_inference,[],[i_0_124,i_0_204,i_0_227,i_0_258,i_0_200,i_0_111,i_0_118,i_0_172,i_0_271,i_0_276,i_0_119,i_0_282,i_0_197,i_0_192,i_0_145,i_0_146,i_0_116,i_0_98,i_0_115,i_0_96,i_0_97,i_0_112,i_0_86,i_0_130,i_0_94,i_0_101,i_0_140]) ).
cnf(i_0_295,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_118]) ).
cnf(i_0_296,plain,
~ subset(set_intersection2(esk7_0,esk9_0),set_intersection2(esk9_0,esk9_0)),
inference(scs_inference,[],[i_0_124,i_0_204,i_0_227,i_0_258,i_0_200,i_0_111,i_0_118,i_0_295,i_0_172,i_0_271,i_0_276,i_0_119,i_0_282,i_0_197,i_0_192,i_0_145,i_0_146,i_0_116,i_0_98,i_0_115,i_0_96,i_0_97,i_0_112,i_0_86,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141]) ).
cnf(i_0_297,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_118]) ).
cnf(i_0_298,plain,
set_intersection2(esk5_0,esk5_0) = set_union2(esk5_0,esk5_0),
inference(scs_inference,[],[i_0_124,i_0_204,i_0_227,i_0_258,i_0_243,i_0_200,i_0_111,i_0_118,i_0_295,i_0_297,i_0_172,i_0_271,i_0_276,i_0_119,i_0_282,i_0_197,i_0_192,i_0_145,i_0_146,i_0_116,i_0_98,i_0_115,i_0_96,i_0_97,i_0_112,i_0_86,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131]) ).
cnf(i_0_299,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_118]) ).
cnf(i_0_300,plain,
~ in(X1,set_intersection2(set_intersection2(esk5_0,esk5_0),set_intersection2(esk5_0,esk5_0))),
inference(scs_inference,[],[i_0_124,i_0_204,i_0_227,i_0_258,i_0_243,i_0_200,i_0_111,i_0_118,i_0_295,i_0_297,i_0_299,i_0_172,i_0_271,i_0_276,i_0_119,i_0_282,i_0_197,i_0_194,i_0_192,i_0_145,i_0_146,i_0_116,i_0_98,i_0_115,i_0_96,i_0_97,i_0_112,i_0_86,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131,i_0_137]) ).
cnf(i_0_301,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_118]) ).
cnf(i_0_302,plain,
~ in(X1,set_union2(set_intersection2(X2,empty_set),set_intersection2(X2,empty_set))),
inference(scs_inference,[],[i_0_124,i_0_204,i_0_227,i_0_258,i_0_243,i_0_200,i_0_111,i_0_118,i_0_295,i_0_297,i_0_299,i_0_172,i_0_271,i_0_276,i_0_279,i_0_119,i_0_282,i_0_197,i_0_194,i_0_192,i_0_145,i_0_146,i_0_116,i_0_98,i_0_115,i_0_96,i_0_97,i_0_112,i_0_86,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131,i_0_137,i_0_88]) ).
cnf(i_0_303,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(rename_variables,[],[i_0_111]) ).
cnf(i_0_304,plain,
( X1 != set_union2(X2,X3)
| in(X4,X2)
| in(X4,X3)
| ~ in(X4,X1) ),
inference(rename_variables,[],[i_0_88]) ).
cnf(i_0_305,plain,
( in(X1,set_union2(set_union2(X2,X3),set_union2(X2,X3)))
| ~ in(X1,X3) ),
inference(scs_inference,[],[i_0_124,i_0_204,i_0_227,i_0_258,i_0_243,i_0_200,i_0_111,i_0_118,i_0_295,i_0_297,i_0_299,i_0_172,i_0_271,i_0_276,i_0_279,i_0_119,i_0_282,i_0_197,i_0_194,i_0_192,i_0_145,i_0_146,i_0_116,i_0_98,i_0_115,i_0_96,i_0_97,i_0_112,i_0_86,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131,i_0_137,i_0_88,i_0_93]) ).
cnf(i_0_306,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_307,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X3) ),
inference(rename_variables,[],[i_0_93]) ).
cnf(i_0_308,plain,
( in(set_intersection2(empty_set,X1),set_union2(set_union2(X2,X3),set_union2(X2,X3)))
| ~ in(empty_set,X3) ),
inference(scs_inference,[],[i_0_124,i_0_178,i_0_204,i_0_227,i_0_258,i_0_243,i_0_200,i_0_111,i_0_118,i_0_295,i_0_297,i_0_299,i_0_172,i_0_271,i_0_276,i_0_279,i_0_119,i_0_282,i_0_197,i_0_194,i_0_192,i_0_145,i_0_146,i_0_116,i_0_98,i_0_115,i_0_96,i_0_97,i_0_112,i_0_86,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131,i_0_137,i_0_88,i_0_93,i_0_136]) ).
cnf(i_0_309,plain,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_311,plain,
~ in(X1,set_intersection2(set_union2(empty_set,empty_set),X2)),
inference(scs_inference,[],[i_0_281,i_0_145]) ).
cnf(i_0_312,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(rename_variables,[],[i_0_145]) ).
cnf(i_0_313,plain,
~ in(X1,set_intersection2(X2,set_union2(empty_set,empty_set))),
inference(scs_inference,[],[i_0_281,i_0_145,i_0_146]) ).
cnf(i_0_314,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(rename_variables,[],[i_0_146]) ).
cnf(i_0_315,plain,
subset(set_union2(esk5_0,esk5_0),set_intersection2(esk5_0,esk5_0)),
inference(scs_inference,[],[i_0_281,i_0_298,i_0_145,i_0_146,i_0_116]) ).
cnf(i_0_316,plain,
( X1 != X2
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_116]) ).
cnf(i_0_317,plain,
subset(set_union2(empty_set,empty_set),X1),
inference(scs_inference,[],[i_0_281,i_0_298,i_0_145,i_0_146,i_0_116,i_0_98]) ).
cnf(i_0_318,plain,
~ in(X1,set_union2(empty_set,empty_set)),
inference(rename_variables,[],[i_0_281]) ).
cnf(i_0_319,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_98]) ).
cnf(i_0_320,plain,
disjoint(set_union2(empty_set,empty_set),X1),
inference(scs_inference,[],[i_0_281,i_0_318,i_0_298,i_0_145,i_0_146,i_0_116,i_0_98,i_0_96]) ).
cnf(i_0_321,plain,
~ in(X1,set_union2(empty_set,empty_set)),
inference(rename_variables,[],[i_0_281]) ).
cnf(i_0_322,plain,
( in(esk10_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_96]) ).
cnf(i_0_323,plain,
disjoint(X1,set_union2(empty_set,empty_set)),
inference(scs_inference,[],[i_0_281,i_0_318,i_0_321,i_0_298,i_0_145,i_0_146,i_0_116,i_0_98,i_0_96,i_0_97]) ).
cnf(i_0_324,plain,
~ in(X1,set_union2(empty_set,empty_set)),
inference(rename_variables,[],[i_0_281]) ).
cnf(i_0_325,plain,
( in(esk10_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_97]) ).
cnf(i_0_326,plain,
disjoint(set_intersection2(esk5_0,esk5_0),set_intersection2(esk5_0,esk5_0)),
inference(scs_inference,[],[i_0_300,i_0_281,i_0_318,i_0_321,i_0_298,i_0_145,i_0_146,i_0_116,i_0_98,i_0_96,i_0_97,i_0_86]) ).
cnf(i_0_327,plain,
~ in(X1,set_intersection2(set_intersection2(esk5_0,esk5_0),set_intersection2(esk5_0,esk5_0))),
inference(rename_variables,[],[i_0_300]) ).
cnf(i_0_328,plain,
( in(esk11_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_329,plain,
subset(set_intersection2(esk5_0,esk5_0),set_union2(esk5_0,esk5_0)),
inference(scs_inference,[],[i_0_300,i_0_281,i_0_318,i_0_321,i_0_298,i_0_145,i_0_146,i_0_116,i_0_98,i_0_96,i_0_97,i_0_86,i_0_115]) ).
cnf(i_0_330,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_115]) ).
cnf(i_0_331,plain,
set_intersection2(empty_set,X1) = esk5_0,
inference(scs_inference,[],[i_0_290,i_0_300,i_0_281,i_0_318,i_0_321,i_0_298,i_0_145,i_0_146,i_0_116,i_0_98,i_0_96,i_0_97,i_0_86,i_0_115,i_0_130]) ).
cnf(i_0_332,plain,
~ subset(set_intersection2(esk7_0,esk9_0),set_intersection2(set_intersection2(esk8_0,esk9_0),X1)),
inference(scs_inference,[],[i_0_84,i_0_103,i_0_290,i_0_300,i_0_281,i_0_318,i_0_321,i_0_298,i_0_145,i_0_146,i_0_116,i_0_98,i_0_96,i_0_97,i_0_86,i_0_115,i_0_130,i_0_94]) ).
cnf(i_0_333,plain,
subset(set_intersection2(X1,X2),X1),
inference(rename_variables,[],[i_0_103]) ).
cnf(i_0_334,plain,
( ~ subset(X1,X2)
| subset(X3,X2)
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_94]) ).
cnf(i_0_335,plain,
set_intersection2(X1,empty_set) = set_intersection2(set_intersection2(X1,empty_set),X2),
inference(scs_inference,[],[i_0_84,i_0_103,i_0_333,i_0_270,i_0_290,i_0_300,i_0_281,i_0_318,i_0_321,i_0_298,i_0_145,i_0_146,i_0_116,i_0_98,i_0_96,i_0_97,i_0_86,i_0_115,i_0_130,i_0_94,i_0_101]) ).
cnf(i_0_336,plain,
subset(set_intersection2(X1,empty_set),X2),
inference(rename_variables,[],[i_0_270]) ).
cnf(i_0_337,plain,
subset(set_intersection2(X1,X2),X1),
inference(rename_variables,[],[i_0_103]) ).
cnf(i_0_338,plain,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_101]) ).
cnf(i_0_339,plain,
~ subset(set_intersection2(esk9_0,esk7_0),set_intersection2(set_intersection2(esk8_0,esk9_0),set_intersection2(esk8_0,esk9_0))),
inference(scs_inference,[],[i_0_84,i_0_184,i_0_103,i_0_333,i_0_270,i_0_290,i_0_110,i_0_300,i_0_281,i_0_318,i_0_321,i_0_298,i_0_145,i_0_146,i_0_116,i_0_98,i_0_96,i_0_97,i_0_86,i_0_115,i_0_130,i_0_94,i_0_101,i_0_140]) ).
cnf(i_0_340,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(rename_variables,[],[i_0_110]) ).
cnf(i_0_341,plain,
~ subset(set_intersection2(esk9_0,esk7_0),set_intersection2(esk9_0,esk8_0)),
inference(scs_inference,[],[i_0_84,i_0_184,i_0_247,i_0_103,i_0_333,i_0_270,i_0_290,i_0_110,i_0_340,i_0_300,i_0_281,i_0_318,i_0_321,i_0_298,i_0_145,i_0_146,i_0_116,i_0_98,i_0_96,i_0_97,i_0_86,i_0_115,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141]) ).
cnf(i_0_342,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(rename_variables,[],[i_0_110]) ).
cnf(i_0_343,plain,
set_intersection2(esk5_0,esk5_0) = set_intersection2(empty_set,X1),
inference(scs_inference,[],[i_0_84,i_0_184,i_0_247,i_0_103,i_0_333,i_0_270,i_0_290,i_0_110,i_0_340,i_0_118,i_0_300,i_0_281,i_0_318,i_0_321,i_0_298,i_0_145,i_0_146,i_0_116,i_0_98,i_0_96,i_0_97,i_0_86,i_0_115,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131]) ).
cnf(i_0_344,plain,
set_intersection2(X1,X1) = X1,
inference(rename_variables,[],[i_0_118]) ).
cnf(i_0_345,plain,
( in(X1,set_union2(set_union2(X2,X3),empty_set))
| ~ in(X1,X2) ),
inference(scs_inference,[],[i_0_84,i_0_184,i_0_247,i_0_103,i_0_333,i_0_270,i_0_290,i_0_110,i_0_340,i_0_118,i_0_300,i_0_281,i_0_318,i_0_321,i_0_298,i_0_121,i_0_145,i_0_146,i_0_116,i_0_98,i_0_96,i_0_97,i_0_86,i_0_115,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131,i_0_92]) ).
cnf(i_0_346,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_121]) ).
cnf(i_0_347,plain,
( X1 != set_union2(X2,X3)
| in(X4,X1)
| ~ in(X4,X2) ),
inference(rename_variables,[],[i_0_92]) ).
cnf(i_0_348,plain,
( in(set_intersection2(empty_set,X1),set_union2(set_union2(X2,X3),empty_set))
| ~ in(empty_set,X2) ),
inference(scs_inference,[],[i_0_84,i_0_178,i_0_184,i_0_247,i_0_103,i_0_333,i_0_270,i_0_290,i_0_110,i_0_340,i_0_118,i_0_300,i_0_281,i_0_318,i_0_321,i_0_298,i_0_121,i_0_145,i_0_146,i_0_116,i_0_98,i_0_96,i_0_97,i_0_86,i_0_115,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131,i_0_92,i_0_136]) ).
cnf(i_0_349,plain,
( ~ disjoint(X1,X2)
| ~ in(X3,X1)
| ~ in(X3,X2) ),
inference(rename_variables,[],[i_0_89]) ).
cnf(i_0_351,plain,
~ in(X1,set_intersection2(X2,set_intersection2(esk5_0,esk5_0))),
inference(scs_inference,[],[i_0_194,i_0_146]) ).
cnf(i_0_352,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(rename_variables,[],[i_0_146]) ).
cnf(i_0_353,plain,
~ in(X1,set_intersection2(set_intersection2(esk5_0,esk5_0),X2)),
inference(scs_inference,[],[i_0_194,i_0_146,i_0_145]) ).
cnf(i_0_354,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(rename_variables,[],[i_0_145]) ).
cnf(i_0_355,plain,
subset(set_intersection2(esk5_0,esk5_0),X1),
inference(scs_inference,[],[i_0_194,i_0_146,i_0_145,i_0_98]) ).
cnf(i_0_356,plain,
~ in(X1,set_intersection2(esk5_0,esk5_0)),
inference(rename_variables,[],[i_0_194]) ).
cnf(i_0_357,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_98]) ).
cnf(i_0_358,plain,
disjoint(set_intersection2(esk5_0,esk5_0),X1),
inference(scs_inference,[],[i_0_194,i_0_356,i_0_146,i_0_145,i_0_98,i_0_96]) ).
cnf(i_0_359,plain,
~ in(X1,set_intersection2(esk5_0,esk5_0)),
inference(rename_variables,[],[i_0_194]) ).
cnf(i_0_360,plain,
( in(esk10_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_96]) ).
cnf(i_0_361,plain,
disjoint(X1,set_intersection2(esk5_0,esk5_0)),
inference(scs_inference,[],[i_0_194,i_0_356,i_0_359,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97]) ).
cnf(i_0_362,plain,
~ in(X1,set_intersection2(esk5_0,esk5_0)),
inference(rename_variables,[],[i_0_194]) ).
cnf(i_0_363,plain,
( in(esk10_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_97]) ).
cnf(i_0_364,plain,
disjoint(esk5_0,esk5_0),
inference(scs_inference,[],[i_0_194,i_0_356,i_0_359,i_0_362,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_86]) ).
cnf(i_0_365,plain,
~ in(X1,set_intersection2(esk5_0,esk5_0)),
inference(rename_variables,[],[i_0_194]) ).
cnf(i_0_366,plain,
( in(esk11_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_367,plain,
subset(X1,set_union2(set_intersection2(X1,X1),set_intersection2(X1,X1))),
inference(scs_inference,[],[i_0_194,i_0_356,i_0_359,i_0_362,i_0_192,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_86,i_0_116]) ).
cnf(i_0_368,plain,
( X1 != X2
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_116]) ).
cnf(i_0_369,plain,
subset(set_union2(X1,empty_set),X1),
inference(scs_inference,[],[i_0_194,i_0_356,i_0_359,i_0_362,i_0_192,i_0_121,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_86,i_0_116,i_0_115]) ).
cnf(i_0_370,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_115]) ).
cnf(i_0_371,plain,
set_intersection2(set_intersection2(X1,empty_set),X2) = set_intersection2(X1,empty_set),
inference(scs_inference,[],[i_0_335,i_0_194,i_0_356,i_0_359,i_0_362,i_0_192,i_0_121,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_86,i_0_116,i_0_115,i_0_130]) ).
cnf(i_0_372,plain,
~ subset(set_intersection2(esk7_0,esk9_0),set_intersection2(empty_set,X1)),
inference(scs_inference,[],[i_0_84,i_0_227,i_0_335,i_0_194,i_0_356,i_0_359,i_0_362,i_0_192,i_0_121,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_86,i_0_116,i_0_115,i_0_130,i_0_94]) ).
cnf(i_0_373,plain,
subset(set_intersection2(empty_set,X1),X2),
inference(rename_variables,[],[i_0_227]) ).
cnf(i_0_374,plain,
( ~ subset(X1,X2)
| subset(X3,X2)
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_94]) ).
cnf(i_0_375,plain,
~ subset(set_intersection2(esk7_0,esk9_0),empty_set),
inference(scs_inference,[],[i_0_84,i_0_227,i_0_103,i_0_335,i_0_194,i_0_356,i_0_359,i_0_362,i_0_192,i_0_121,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_86,i_0_116,i_0_115,i_0_130,i_0_94,i_0_83]) ).
cnf(i_0_376,plain,
subset(set_intersection2(X1,X2),X1),
inference(rename_variables,[],[i_0_103]) ).
cnf(i_0_377,plain,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_378,plain,
set_intersection2(set_intersection2(empty_set,X1),X2) = set_intersection2(empty_set,X1),
inference(scs_inference,[],[i_0_84,i_0_227,i_0_373,i_0_103,i_0_376,i_0_335,i_0_194,i_0_356,i_0_359,i_0_362,i_0_192,i_0_121,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_86,i_0_116,i_0_115,i_0_130,i_0_94,i_0_83,i_0_101]) ).
cnf(i_0_379,plain,
subset(set_intersection2(X1,X2),X1),
inference(rename_variables,[],[i_0_103]) ).
cnf(i_0_380,plain,
subset(set_intersection2(empty_set,X1),X2),
inference(rename_variables,[],[i_0_227]) ).
cnf(i_0_381,plain,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_101]) ).
cnf(i_0_382,plain,
~ subset(set_union2(set_intersection2(esk7_0,esk9_0),set_intersection2(esk7_0,esk9_0)),set_intersection2(esk8_0,esk9_0)),
inference(scs_inference,[],[i_0_84,i_0_227,i_0_373,i_0_103,i_0_376,i_0_335,i_0_119,i_0_194,i_0_356,i_0_359,i_0_362,i_0_192,i_0_121,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_86,i_0_116,i_0_115,i_0_130,i_0_94,i_0_83,i_0_101,i_0_140]) ).
cnf(i_0_383,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_384,plain,
~ subset(set_intersection2(esk7_0,esk9_0),set_union2(set_intersection2(esk8_0,esk9_0),set_intersection2(esk8_0,esk9_0))),
inference(scs_inference,[],[i_0_84,i_0_227,i_0_373,i_0_103,i_0_376,i_0_335,i_0_119,i_0_383,i_0_194,i_0_356,i_0_359,i_0_362,i_0_192,i_0_121,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_86,i_0_116,i_0_115,i_0_130,i_0_94,i_0_83,i_0_101,i_0_140,i_0_141]) ).
cnf(i_0_385,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_386,plain,
set_union2(esk5_0,esk5_0) = set_intersection2(empty_set,X1),
inference(scs_inference,[],[i_0_84,i_0_290,i_0_227,i_0_373,i_0_103,i_0_376,i_0_335,i_0_119,i_0_383,i_0_385,i_0_194,i_0_356,i_0_359,i_0_362,i_0_192,i_0_121,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_86,i_0_116,i_0_115,i_0_130,i_0_94,i_0_83,i_0_101,i_0_140,i_0_141,i_0_131]) ).
cnf(i_0_387,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_388,plain,
~ in(X1,set_union2(esk5_0,esk5_0)),
inference(scs_inference,[],[i_0_84,i_0_290,i_0_227,i_0_373,i_0_103,i_0_376,i_0_335,i_0_119,i_0_383,i_0_385,i_0_387,i_0_194,i_0_356,i_0_359,i_0_362,i_0_162,i_0_192,i_0_121,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_86,i_0_116,i_0_115,i_0_130,i_0_94,i_0_83,i_0_101,i_0_140,i_0_141,i_0_131,i_0_137]) ).
cnf(i_0_389,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_119]) ).
cnf(i_0_390,plain,
set_intersection2(esk5_0,esk5_0) = empty_set,
inference(scs_inference,[],[i_0_84,i_0_290,i_0_227,i_0_373,i_0_103,i_0_376,i_0_335,i_0_119,i_0_383,i_0_385,i_0_387,i_0_194,i_0_356,i_0_359,i_0_362,i_0_162,i_0_192,i_0_121,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_86,i_0_116,i_0_115,i_0_130,i_0_94,i_0_83,i_0_101,i_0_140,i_0_141,i_0_131,i_0_137,i_0_114]) ).
cnf(i_0_391,plain,
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_392,plain,
set_union2(set_intersection2(X1,X1),set_intersection2(X1,X1)) = X1,
inference(rename_variables,[],[i_0_192]) ).
cnf(i_0_393,plain,
( in(X1,set_union2(set_intersection2(set_intersection2(X2,X3),set_intersection2(X2,X3)),set_intersection2(set_intersection2(X2,X3),set_intersection2(X2,X3))))
| ~ in(X1,X2)
| ~ in(X1,X3) ),
inference(scs_inference,[],[i_0_84,i_0_290,i_0_227,i_0_373,i_0_103,i_0_376,i_0_335,i_0_119,i_0_383,i_0_385,i_0_387,i_0_194,i_0_356,i_0_359,i_0_362,i_0_162,i_0_192,i_0_121,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_86,i_0_116,i_0_115,i_0_130,i_0_94,i_0_83,i_0_101,i_0_140,i_0_141,i_0_131,i_0_137,i_0_114,i_0_85]) ).
cnf(i_0_394,plain,
~ in(X1,set_intersection2(X2,esk5_0)),
inference(scs_inference,[],[i_0_162,i_0_146]) ).
cnf(i_0_395,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(rename_variables,[],[i_0_146]) ).
cnf(i_0_396,plain,
~ in(X1,set_intersection2(esk5_0,X2)),
inference(scs_inference,[],[i_0_162,i_0_146,i_0_145]) ).
cnf(i_0_397,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(rename_variables,[],[i_0_145]) ).
cnf(i_0_398,plain,
subset(set_union2(esk5_0,esk5_0),X1),
inference(scs_inference,[],[i_0_162,i_0_388,i_0_146,i_0_145,i_0_98]) ).
cnf(i_0_399,plain,
~ in(X1,set_union2(esk5_0,esk5_0)),
inference(rename_variables,[],[i_0_388]) ).
cnf(i_0_400,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_98]) ).
cnf(i_0_401,plain,
disjoint(esk5_0,X1),
inference(scs_inference,[],[i_0_162,i_0_388,i_0_146,i_0_145,i_0_98,i_0_96]) ).
cnf(i_0_402,plain,
~ in(X1,esk5_0),
inference(rename_variables,[],[i_0_162]) ).
cnf(i_0_403,plain,
( in(esk10_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_96]) ).
cnf(i_0_404,plain,
disjoint(X1,esk5_0),
inference(scs_inference,[],[i_0_162,i_0_402,i_0_388,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97]) ).
cnf(i_0_405,plain,
~ in(X1,esk5_0),
inference(rename_variables,[],[i_0_162]) ).
cnf(i_0_406,plain,
( in(esk10_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_97]) ).
cnf(i_0_407,plain,
set_intersection2(empty_set,X1) = set_intersection2(set_intersection2(empty_set,X1),X2),
inference(scs_inference,[],[i_0_378,i_0_162,i_0_402,i_0_388,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_130]) ).
cnf(i_0_408,plain,
~ subset(set_intersection2(esk7_0,esk9_0),esk5_0),
inference(scs_inference,[],[i_0_84,i_0_200,i_0_378,i_0_162,i_0_402,i_0_388,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_130,i_0_94]) ).
cnf(i_0_409,plain,
subset(esk5_0,X1),
inference(rename_variables,[],[i_0_200]) ).
cnf(i_0_410,plain,
( ~ subset(X1,X2)
| subset(X3,X2)
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_94]) ).
cnf(i_0_411,plain,
X1 = set_union2(set_intersection2(X1,X1),set_intersection2(X1,X1)),
inference(scs_inference,[],[i_0_84,i_0_200,i_0_273,i_0_367,i_0_378,i_0_162,i_0_402,i_0_388,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101]) ).
cnf(i_0_412,plain,
subset(X1,set_union2(set_intersection2(X1,X1),set_intersection2(X1,X1))),
inference(rename_variables,[],[i_0_367]) ).
cnf(i_0_413,plain,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_101]) ).
cnf(i_0_414,plain,
~ subset(set_intersection2(esk9_0,esk7_0),set_intersection2(esk9_0,esk9_0)),
inference(scs_inference,[],[i_0_84,i_0_296,i_0_200,i_0_273,i_0_367,i_0_378,i_0_110,i_0_162,i_0_402,i_0_388,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101,i_0_140]) ).
cnf(i_0_415,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(rename_variables,[],[i_0_110]) ).
cnf(i_0_416,plain,
~ subset(set_intersection2(esk9_0,esk7_0),set_union2(esk7_0,empty_set)),
inference(scs_inference,[],[i_0_84,i_0_296,i_0_200,i_0_273,i_0_367,i_0_378,i_0_288,i_0_110,i_0_121,i_0_162,i_0_402,i_0_388,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141]) ).
cnf(i_0_417,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_121]) ).
cnf(i_0_418,plain,
set_union2(esk5_0,empty_set) = set_intersection2(empty_set,X1),
inference(scs_inference,[],[i_0_84,i_0_290,i_0_296,i_0_200,i_0_273,i_0_367,i_0_378,i_0_288,i_0_110,i_0_121,i_0_417,i_0_162,i_0_402,i_0_388,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131]) ).
cnf(i_0_419,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_121]) ).
cnf(i_0_420,plain,
~ in(X1,set_union2(esk5_0,empty_set)),
inference(scs_inference,[],[i_0_84,i_0_290,i_0_296,i_0_200,i_0_273,i_0_367,i_0_378,i_0_288,i_0_110,i_0_121,i_0_417,i_0_419,i_0_162,i_0_402,i_0_405,i_0_388,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131,i_0_137]) ).
cnf(i_0_421,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_121]) ).
cnf(i_0_422,plain,
set_union2(esk5_0,esk5_0) = empty_set,
inference(scs_inference,[],[i_0_84,i_0_290,i_0_296,i_0_200,i_0_273,i_0_367,i_0_378,i_0_288,i_0_110,i_0_121,i_0_417,i_0_419,i_0_162,i_0_402,i_0_405,i_0_388,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131,i_0_137,i_0_114]) ).
cnf(i_0_423,plain,
( ~ subset(X1,empty_set)
| X1 = empty_set ),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_424,plain,
subset(set_union2(esk5_0,empty_set),set_intersection2(empty_set,X1)),
inference(scs_inference,[],[i_0_84,i_0_290,i_0_296,i_0_200,i_0_273,i_0_367,i_0_378,i_0_288,i_0_110,i_0_121,i_0_417,i_0_419,i_0_162,i_0_402,i_0_405,i_0_388,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131,i_0_137,i_0_114,i_0_115]) ).
cnf(i_0_425,plain,
( X1 != X2
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_115]) ).
cnf(i_0_426,plain,
( ~ subset(set_union2(set_intersection2(esk7_0,esk9_0),set_intersection2(esk7_0,esk9_0)),esk8_0)
| ~ subset(set_union2(set_intersection2(esk7_0,esk9_0),set_intersection2(esk7_0,esk9_0)),esk9_0) ),
inference(scs_inference,[],[i_0_84,i_0_290,i_0_296,i_0_200,i_0_273,i_0_367,i_0_378,i_0_288,i_0_382,i_0_110,i_0_121,i_0_417,i_0_419,i_0_162,i_0_402,i_0_405,i_0_388,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101,i_0_140,i_0_141,i_0_131,i_0_137,i_0_114,i_0_115,i_0_83]) ).
cnf(i_0_427,plain,
( subset(X1,set_intersection2(X2,X3))
| ~ subset(X1,X2)
| ~ subset(X1,X3) ),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_428,plain,
subset(set_intersection2(esk7_0,X1),esk8_0),
inference(rename_variables,[],[i_0_175]) ).
cnf(i_0_429,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_121]) ).
cnf(i_0_430,plain,
set_union2(X1,empty_set) = X1,
inference(rename_variables,[],[i_0_121]) ).
cnf(i_0_431,plain,
~ in(X1,set_intersection2(set_intersection2(empty_set,X2),X3)),
inference(rename_variables,[],[i_0_215]) ).
cnf(i_0_433,plain,
~ in(X1,set_intersection2(X2,set_intersection2(X3,esk5_0))),
inference(scs_inference,[],[i_0_394,i_0_146]) ).
cnf(i_0_434,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(rename_variables,[],[i_0_146]) ).
cnf(i_0_435,plain,
~ in(X1,set_intersection2(set_intersection2(X2,esk5_0),X3)),
inference(scs_inference,[],[i_0_394,i_0_146,i_0_145]) ).
cnf(i_0_436,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(rename_variables,[],[i_0_145]) ).
cnf(i_0_437,plain,
subset(set_intersection2(X1,esk5_0),X2),
inference(scs_inference,[],[i_0_394,i_0_146,i_0_145,i_0_98]) ).
cnf(i_0_438,plain,
~ in(X1,set_intersection2(X2,esk5_0)),
inference(rename_variables,[],[i_0_394]) ).
cnf(i_0_439,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_98]) ).
cnf(i_0_440,plain,
disjoint(set_intersection2(X1,esk5_0),X2),
inference(scs_inference,[],[i_0_394,i_0_438,i_0_146,i_0_145,i_0_98,i_0_96]) ).
cnf(i_0_441,plain,
~ in(X1,set_intersection2(X2,esk5_0)),
inference(rename_variables,[],[i_0_394]) ).
cnf(i_0_442,plain,
( in(esk10_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_96]) ).
cnf(i_0_443,plain,
disjoint(X1,set_intersection2(X2,esk5_0)),
inference(scs_inference,[],[i_0_394,i_0_438,i_0_441,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97]) ).
cnf(i_0_444,plain,
~ in(X1,set_intersection2(X2,esk5_0)),
inference(rename_variables,[],[i_0_394]) ).
cnf(i_0_445,plain,
( in(esk10_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(rename_variables,[],[i_0_97]) ).
cnf(i_0_446,plain,
set_intersection2(empty_set,X1) = set_intersection2(X2,empty_set),
inference(scs_inference,[],[i_0_251,i_0_394,i_0_438,i_0_441,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_130]) ).
cnf(i_0_447,plain,
~ subset(set_intersection2(esk9_0,esk7_0),set_union2(empty_set,esk7_0)),
inference(scs_inference,[],[i_0_268,i_0_416,i_0_251,i_0_394,i_0_438,i_0_441,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_130,i_0_94]) ).
cnf(i_0_448,plain,
subset(set_union2(X1,X2),set_union2(X2,X1)),
inference(rename_variables,[],[i_0_268]) ).
cnf(i_0_449,plain,
( ~ subset(X1,X2)
| subset(X3,X2)
| ~ subset(X3,X1) ),
inference(rename_variables,[],[i_0_94]) ).
cnf(i_0_450,plain,
set_union2(empty_set,empty_set) = set_intersection2(empty_set,X1),
inference(scs_inference,[],[i_0_227,i_0_268,i_0_317,i_0_416,i_0_251,i_0_394,i_0_438,i_0_441,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101]) ).
cnf(i_0_451,plain,
subset(set_union2(empty_set,empty_set),X1),
inference(rename_variables,[],[i_0_317]) ).
cnf(i_0_452,plain,
subset(set_intersection2(empty_set,X1),X2),
inference(rename_variables,[],[i_0_227]) ).
cnf(i_0_453,plain,
( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_101]) ).
cnf(i_0_454,plain,
$false,
inference(scs_inference,[],[i_0_227,i_0_103,i_0_268,i_0_317,i_0_414,i_0_416,i_0_251,i_0_394,i_0_438,i_0_441,i_0_146,i_0_145,i_0_98,i_0_96,i_0_97,i_0_130,i_0_94,i_0_101,i_0_83]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU129+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n028.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:45:01 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 0.51/1.60 % Version : CSE_E---1.7
% 0.51/1.60 % Problem : theBenchmark.p
% 0.51/1.60 % SZS status Theorem for theBenchmark.p
% 0.51/1.60 % SZS output start CNFRefutation
% See solution above
% 1.11/2.29 % Total time : 1.272s
%------------------------------------------------------------------------------